Triangle Polymeters Sound UNHINGED
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- čas přidán 27. 05. 2024
- The Pythagorean theorem is a banger!
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7th grade teacher: “Ben, if side A is 4 and side B is 5, what’s side C?”
Ben: “F#! No wait, G!”
Jon Finn: King of music and of jokes!
b6
3 over 4 over 5 is a certified banger
It's sooo cool!
Absolutely. I keep going back to listen to that segment over and over. I want a full track from that little 1:12-1:29 clip
Yep
He is playing meshuggah
Fun fact (maybe) it's the ratio of a major chord
Heard about Math Rock but Ben here is creating trigonometry rock!
Let's switch to pythagorean tuning and make it complete!
@@ontoverse And only use sawtooth waves
Good luck actually playing that (unless you're Sungazer)
I'd have to program it in a sequencer that could do that, and then mute one "side" and try to jam along. Or else, play all 3 and try to jam along to THAT... but I don't know whether it's possible, especially with note number instead of just rhythm.
Sounds like Palm to me. RIP
man i love sungazer
came to say the same thing - clip at the end giving me palm vibes!
@@jm-wd6up Had no clue they broke up til I read your comment, rip palm
Ben Levin + math rock???
this must be my birthday
happy birthday !
The coolest thing I found is that the short side "acts" as the pulse which makes it actually danceable music :) Now go completely triangle-crazy and incorporate the angles, the area of the triangle, and the areas of the squares used to fulfill the theorem.
This is the most underrated music channel of all time.
You could use different rows of pascal's triangle to generate cool rhythms. all the rows add up to powers of 2 as well so it should be really easy to fit into a song with a 4/4 time signature, or something similar. I think it would be cool if you did more math-fueled compositions, Ben.
could you give an example?
@@pez1870 yeah sure. pascals triangle looks like this:
1
1 1
1 2 1
1 3 3 1
1 4 6 4 1
1 5 10 10 5 1
etc.
you could imagine maybe making a bassline that uses the 5th row, 1 4 6 4 1, where the numbers represent the number of quarter notes you hold a specific note for, and then above that, you could use the 1 5 10 10 5 1 row to make a melody where each number represents the number of eighth notes each note is held, and so on. This is just one idea though. You could also use the numbers to represent scale degrees, so each row of the triangle can represent a melody that you can use multiple times throughout a composition. theres a few ways to use it but it would be cool to see what someone who's better at music than I am can do with it.
I love this idea.
This is my 19th video in a row! If you'd like to help me keep the streak going, checkout www.Patreon.com/BenLevin
I love the touch with the animated eyes in this video!
i feel like this is what insanity sounds like
That 3 4 5 is some good djenting. Feels intuitive, visceral, true.
I like the idea of mapping it to semitones, but maybe multiples of a fundamental (harmonics) or just intonation ratios would be more consonant?
Either way i think you really discovered something here!
i thought about that too
One of the things I do when I'm stuck is I'll pull up the digits of pi converted to base-12 or base-8 and grab a random section of 5-20-ish notes and try to incorporate it into the music somehow.
I bet that's another video one of these days
Critics described Autechre's rhythms as geometric. Now I finally know what trigonometric rhythms sound like!
This was fascinating and inspiring, Ben! Thanks for sharing!
dude i absaloutly love you, your recnet videos are ceative af
also love your music✌✌
This is the best music! I have these sorts of ideas all the time but very few make it very far. You made them sound so cool!
Yes Ben!!
I love this idea Ben!!!
Very cool Ben!
I love this channel soo much
I have taken Ben's course and you should too. Fun and engaging, it really covers a lot of ground. Worth it!
These videos deserve so many more views. I love them ,,
unique sound unique process. i love this!
This is the coolest thing ever ! Im gonna try this with my ideas.
Rock on Ben!
Sounds rad!
How clever using triangles! The 3+4+5 sounds very proggy. Reminds me of the start of the bridge section of Anesthetize by Porcupine Tree
I very much enjoyed this.
great creativity you got going on there
Hey Ben! For what it’s worth, I saw this video popped up a bit ago, but didn’t click it until you switched the title. Nice title-and nice video!
Trig rock! That's awesome. 3-4-5 is very pleasing to the ear.
How about something fun? Complex algebra mapping 2D rotations to pitch or rhythm changes?
Something about this really made it sink in for me how different polyrhythms and polymeters sound. Something about hearing 3 or more at a time made it all make more sense. It’s so weird because I’ve been through a music undergrad and they never showed this to me.
very cool ben
so fucking great and inspiring love u ben
8-15-17 becomes almost a disco beat I love it
Awesome.
this is cool as shit Ben, hell yeah dude
Maths and music, fascinating subject. One of my examples, is audio distortion. Take some trig function and an audio input, take the inverse of that trig function, yes complex numbers typically needed, mess with the gains of the complex numbers that result, then apply the trig function again and output as the distorted signal. Thanks Ben, love the rhythms from your triangles.
masterful
01:10 we need a full song of that
Cant wait for the Euclidean rhythm vid
nice exploration Ben! your examples of a math rock band playing the various triangles started to sound like a Horse Lords record. check out the album Common Task for lots of polymeter/polyrhythms, and microtonality and just intonation. nerdy, fun, hypnotic music
I love these sorts of "overly calculated" musical experiments, usually produces some really cool new ideas. Since you asked for other ways to use basic math, a few months ago I had the idea to start using algebra in writing for a similar "plug in values and see what pops out" approach.
The basic idea is that the variables are manually written measures and then you plug them into different equations to transform them. So like "A+3" is taking your A phrase and adding 3 counts to it, "2A+(B-1)" is playing two bars of A followed by one of B missing a count. Deciding what each function even does is half the creative process, I didn't quite get around to working out multiplying measures by each other, squaring, dividing and such but there's a lot of stupid space to explore here.
Nothing too interesting so far, but where I think it potentially shines is when you have a list of equations and then run through them multiple times while changing the variables. Like if you write three phases, the first time through 1 would be A, 2 would be B and 3 would be C. However, the next time through you could have 1 be B, 2 be C and 3 be A, then later 1 is C, 2 is A and 3 is B. It's still nothing you couldn't do without the algebra, but seeing how the transformations affect each phrase in each position is pretty neat and makes it easy to organize what will probably turn out to be a very angular and awkward mathy mess.
Awesome
that was actually beautiful
Damn that 5 against 12 bangs hard!
Really cool! I experimented with something similar a while back, but with 4x 4/16 notes playing, then an additional 3x 3/16 notes, while 5x 5/16 notes play the whole time. Because it’s a Pythagorean triplet, all the rhythms meet up at 25/16! I’ve gotta get around to uploading it
Hi Ben! I recently experimented with a concept I think you'd appreciate. Taking inspiration from the practice of breaking complex time signatures into groups of threes and twos, I wondered what it'd be like to use groups of other sizes. Doing it with groups of fives and threes (at double tempo or thereabouts), for example, gives something like a variation on a swing feeling, though it's different from normal swing rhythms because the pattern can do more than just alternate between long and short groups. Anyway, that was something I found really interesting, thought you'd appreciate it and find it similarly interesting.
Theres an awesome equation (its not taught in high school but its pretty simple) thats:
x_(n+1) = rx_n(1 - x_n)
It is used most commonly to model populations of animals. x_n is the population of generation n, r is the birth rate of the animal (how many offspring a given animal produces) and then the equation gives you the population of generation n+1 (or the next genration). This is linked to chaos theory (think butterfly effect) and could be used to make some interesting and quite poetic music. Maybe something about the ebb and flow of time and life?
Awesome video Ben!
Just make sure r > 3.58
Pretty boring otherwise.
@ontoverse yes should have mentioned that
Sounds like a module that someone would build for Eurorack... organismuc generative triggers
I never thought of using recursion relations in music. That's a cool idea.
This heads into mutant gamelan territory. '80s King Crimson did some of the earliest math rock like this.
Finally, you have invented the Shaggs!
When dabbling into such polymeters, I always find useful to displace a large group by half its length (for example 24,25 - start the snare 12 beats later), it gives some interesting effects
I do like it
Taking two things that seem unrelated on the surface and finding out how they can relate anyway. This is always fun!
Around the 5 minutes mark it sounds like a Palm song
Now use other right triangles like 30, 60, 90s and 45, 45, 90s
The lengths wouldn't be whole numbers.
i like to think of some risers as good examples of exponential functions with the amount of notes getting infinitely larger as time progresses
This reminds me a bit of Henry Cowell's Scales of Rhythm from New Musical Resources.
Palm's been real quiet since this dropped
The only thing I might consider is keeping the drums super-straight. Having the polymeters over a (roughly) 4/4 groove might help to highlight how odd they are while still giving the listener something to anchor to.
Go even further and set the internal angles of the triangle to correlate to something. I'm a software synth kind of guy, so my first thought was attaching angle values to automate synth parameters/macros, either by setting the values to be specific to each triangle, or by having these parameters on an LFO whose speed is determined by angle size.
This gets pretty interesting if you're using the numbers to determine pitch as members of the overtone series rather than semitones. The detuned octaves of 8-15-17 are something to behold.
They more you listen to stuff like this, the less crazy it sounds
The same numeric series can be interpreted in two rather sensible ways! Consider 3:4:5.
One way is this: 3/3, 4/3, 5/3. The other way is 5/5, 5/4, 5/3.
With 4:5:6, the first structure gives the major chord, the second structure gives the minor chord! 4/4, 5/4, 6/4 = major, 6/6, 6/5, 6/4 = minor.
It should likewise be possible to create "major-like" and "minor-like" polymeters out of triangular numbers!
5:30
Once, when I was messing around with my daw, I made a riff inspired by the graph of a sum of sin waves I made while I was messing with a graphing calculator. I dont remember the exact sum tho.
This reminds me of an EQD Rainbow Machine 😄
That sounds like anxiety then organization then anxiety again :D
One of my favorite exercises for exploration is to take pi, e, and sqrt of 2, convert them into base 13 and then applying the digits to a musical component like a cypher: tones (12 pitches and a space), note-lengths, number of measures between tempo variations, dynamic indicators (transitions allowed), etc. But, I'm a nerd.
I programmed a midi piano piece like this with prime numbers sometimes ago. It sounds kinda cool, too bad I didn't upload it anywhere but it's easy to make yourself.
Start on a really high and short note with duration of 2 unit (could be 2 * 16th note), play the complete polymeter pattern for that prime number times, then add a new note with pitch down a fifth and next prime number duration. The low notes get longer and longer as the sequence goes 2 3 5 7 11 13... eventually I stopped at the 11th prime.
A thing to consider is, as the notes go lower, you may need to turn down the velocity/volume of the upper notes, otherwise they will sound too dissonant; with lower volume they blend nicely as ambient percussion noises. I did that by automate PianoTeq's low/high note weighting or something.
This is maybe playable by one or two humans.
Supercollider is a cool tool to do things like that
8 24 25 feels like alien big bad starting a monolog which starts tangenting off
How would you change chords on a per triangle basis? Wait around for the unison?
How would you change rhythm? Maybe you could take the point of greatest distance between the beat of two sides of a triangle and then pivot into the greatest distance between beats of a different rhythm? You could combine that with a chord change for maximum instability.
What would be interesting is to have all of the triangle/chord combos shift around. So take your three triangles and follow some set of transformation rules such that each triangle takes on the characteristics of the others over time.
Then of course you need lyrics set to one of the pulses ala pass the goddamn butter, only more unhinged.
Pretty wild
I've done similar explorations playing around with the software Midinous (with which I am not affiliated). Might be worth taking a look at if you want to do more with this kind of thing.
I love Midinous! I'm currently not letting myself have Steam downloaded on my computer, but I believe they are releasing a version that can run without Steam in the next patch, so I'll definitely be using it for MOST OF MY MUSIC at that point haha!
This toon shader looks really good on your lil‘ guys (I don‘t know their name)
"The Fourth Wall Will Not Protect You" by Yowie is 3:4:5. Bass in 4, drums in 3, guitar in 5. I think they might swap here and there too.
Crazy how little difference there is between genius and the first time you get on fl studio and start clicking away on the beat grid or piano roll
I'm not sure what mathematical technique I'd use, but I'd definitely divide the result by pi.
Euclid's Orchard has been relatively silent since this dropped...🌝
sounds like Palm at the end. lol.
Cool. Regarding mapping the numbers to notes, you used a fixed approach. I wonder what various continuous approaches would produce. For example, lets say your palette of notes spans 2 or 3 octaves (and then loops around). For the first round you used the number to define an interval from C. Suppose each time you play the requisite number of notes, you use the number to bump up the interval from where it was. So, for example, if the number was 5, the first 5 times you play F (5 half steps from C). Maybe for the next 5 you go an additional 5 half steps up to Bb. This approach keeps the whole sound shifting. I'm sure it would eventually repeat but it would take a while. And for the whole sequence with 3 triangles to repeat it would be a very long time. I suppose you could try assigning diatonic chords vs just notes too. Maybe have two of the 3 triangles just using notes and the 3rd one playing diatonic chords (and rotate the role of the "chord playing triangle" periodically). The possible experiments are limitless.
Combinatorics is usually the go to place to check
Man, this got me thinking, what about tuples representing higher order shapes (like quadrilaterals?), and different metrics? More than two dimensions?
tool does fibonacci, you do pythagoras. neat! what's next? thales and archimedes? gauß and euler? :D
3, 4, 5 sounds like an EBM Song of the 90s 😎
Man, i really miss sound shapes
1:13 sounds like Battles!
Dude!! =)
You’ve heard of math rock, but what about geometry rock?
13:4 is my fav polytrhythm
it's just an almost triplet
Well, you gotta use the Pythagorean tuning, too
3:4:5 polyrythm if speed up to audio rate is percieved as major chord (In first inversion)
8-15-17 FTW!
the 3 4 5 rhythm actually sounds familiar.
awesome! though, arent these polyrhythms? polymeter's beat would align, while these drift
also, maybe note ratios would work well instead of steps? like how a fourth from the root is a 4/3 ratio, and a 6th is a 5/3 (and the ratio between those make a 5/4 ratio!)- this chord actually really is just a sped up 3:4:5 polyrythm!
I think you'd be better served looking at number theory rather than geometry, since that's where the explanation lies for the various rhythmic effects (and to some extent the pitches, though there's a wrench in the works there from the almost total arbitrariness of 12EDO).
The proof of this is that most right triangles have ratios like 2:3:3.605551275… or 9:11:14.212670403…, where the rhythm of at least one of the legs _never_ wraps back into sync-unlike, say, the 3,4,5 example, which is a simple pattern of length 60.
In any case, to do the experiment without needing any fancy maths, I'd suggest breaking out the D&D dice and rolling them to get some small integers to try, rather than thinking about triangles.
i would pay for this if you could make your eyebrows do these polyrhythms.
What would happen if you created arpeggios, melodies, harmonies, progressions to each single count with different or the same instruments then smooshed them all back together in song?